1. Field of the Invention
This invention relates to a GaN single crystal substrate, a method of growing a GaN single crystal and a method of making a GaN single crystal substrate which is used for producing light emitting devices, for example, light emitting diodes (LEDs) and laser diodes (LDs).
This application claims the priority of Japanese Patent Application No.11-273882 (273882/1999) filed Sep. 28, 1999 which is incorporated herein by reference.
2. Description of Related Art
Light emitting devices based upon group III-V nitride semiconductors (GaN, GaInN) have been put into practice, in the field of blue light LEDs (light emitting diodes). Since wide gallium nitride (GaN) substrates cannot be produced, the nitride semiconductor devices (blue light LEDs) have been produced upon sapphire substrates (Al2O3). Sapphire crystal (Al2O3) belongs to hexagonal symmetry group. The c-plane (0001) has six-folding rotation symmetry. Thin films of GaN or GaInN are heteroepitaxially grown upon the sapphire substrates for making GaInN type blue light LEDs. The GaN films or GaInN films grown on the sapphire substrates are suffering from a large number of dislocations of about 109 cmxe2x88x922. Despite the high dislocation density, the GaInN/sapphire LEDs made by piling GaN films and GaInN films on the sapphire substrates exhibit high blue light power and a long lifetime as blue light LEDs. The high density of dislocations in the GaN or GaInN films is not a hindrance to the GaInN/sapphire LEDs. Sapphire is sturdy and strong chemically and physically and refractory (high heat-resistance). The sapphire substrate is a very hard and stable material. The advantages allow sapphire to exclusively serve substrates to the GaInN-type blue light LEDs.
The sapphire substrates have still drawbacks. The sapphire substrate has no cleavage plane which would enable device makers to cut a processed wafer into individual chips in exact orientations along the natural cleavage planes without difficulty. Unlike traditional semiconductor wafers, the lack of cleavage forces the device makers to dice the sapphire wafer lengthwise and crosswise with a dicing machine. The dicing step raises the cost of production for making LEDs. In the case of making laser diodes in future, the lack of cleavage will prohibit the makers from forming a pair of mirrors as a resonator by natural cleavage. The resonators made by polishing incur problems in quality and raise the cost of manufacturing. A further drawback is the fact that the sapphire substrate is an insulator.
The insulating substrate invites various problems on electrode fabrication. Unlike a conventional conductive substrate, the bottom of the sapphire substrate cannot be an electrode. In stead of the bottom, a part of a middle layer is exposed by polishing partially the top of a GaN chip for serving a room for an n-electrode. Connection between the LED electrodes and leads requires wirebonding two times per chip. The electric current flows in the horizontal direction in the intermediate GaN layer having the lower electrode. The GaN intermediate layer should be allocated with a sufficient large thickness for decreasing electric resistance. Two electrodes made on the top require a wide area for the LED chip. The GaN devices on the sapphire substrates are suffering from high cost.
Silicon carbide (SiC) substrates have been proposed for the GaN devices for solving the problems accompanying the sapphire substrates. SiC has natural cleavage planes which allow device makers to cut a SiC wafer along the natural cleavage lines in exact orientations without difficulty. The SiC substrate would solve the problems of the dicing step and the resonators of LDs. SiC has good electric conduction which allows a substrate bottom to become a lower electrode. The bottom electrode can reduce the space occupied by the electrodes. A single wirebonding connects the top electrode to the lead. In spite of the convenient properties, SiC is far more expensive than sapphire. SiC is difficult to obtain due to poor supply of SiC. Poor supply of SiC would invite high cost and instability in quality. Further, a GaN film grown upon the SiC substrate still has a problem in quality which is not solved at present. The high cost still inhibits the SiC substrate from bringing GaInN/SiC blue light LEDs into practice.
Crystallographical problems should be pointed out. Heteroepitaxial growth of GaN single crystal films upon sapphire substrates or silicon carbide substrates introduces many defects, e.g., dislocations into the film crystals due to the misfit of lattice structures between the films and the substrates. Different lattice constants degrade the property of the grown crystals. Indeed, it is said that the epitaxial layers of GaN or GaInN upon sapphire substrates on sale should include very high density of dislocations of about 109 cmxe2x88x922.
In the case of the silicon carbide substrates, they say that the GaN or GaInN layers should contain high dislocation density of about 108 cm 2.
Such high density of dislocation would fully deprive Si or GaAs devices of all the desired functions in the case of the Si or GaAs semiconductor devices. Defects are fatal for Si or GaAs crystals. Device fabrication on state of art requires dislocation-free crystals for Si and low dislocation density crystals for GaAs. Low dislocation density or non-dislocation density is indispensable for the preceding Si devices or GaAs devices.
To our surprise, GaN(GaInN) blue light LEDs function quite well despite of such high dislocation density. Many dislocations do not impede the device makers from bringing the GaN type LEDs into practice. Plenty of dislocations do not invite degradation of the LEDs. The GaInN type blue light LEDs are not annoyed at the high dislocation density at present.
The high dislocation density of the crystals induces few problems on the GaN LEDs, because the current density is small in the LEDs. However, such high density of dislocations will induce difficulties in the case of LDs (laser diodes) which require far larger current density than LEDs. The high current density facilitates the degradation originating from the defects in a short time. Current GaInN blue light LDs made upon sapphire substrates are still suffering from a short lifetime. The GaInN blue light LDs have not attained to the practical level yet due to the rapid degradation and the short lifetime in contradiction to the GaInN LEDs. 109 cmxe2x88x922 dislocations seem to reduce the lifetime of the GaInN LDs. The sapphire substrates originate plenty of dislocations in the GaN and GaInN layers grown on the substrates.
The Inventors of the present invention think that the best substrate for the GaN devices should be a GaN single crystal substrate. The adoption of GaN single crystals as the substrates should entirely solve the problem of the mismatching of the lattice constant. The GaN single crystal has cleavage unlike sapphire. Natural cleavage will facilitate to cut a processed wafer into individual device chips. Natural cleavage will replace the dicing step. The cleavage planes will be assigned as the mirrors of resonators in the case of making GaInN laser diodes (LDs). Unlike sapphire, GaN crystal has electric conductivity which simplifies the structure of electrodes by allowing the crystal to assign an n-electrode on the bottom. GaN single crystal is the best candidate for the substrate for growing the GaN or GaInP layers. However, the GaN single crystal has not been used as the substrate for the GaN-type LEDs or LDs. Why has GaN not been adopted yet? The reason is that large GaN single crystals have never been made. The difficulty of making the GaN single crystal forces the adoption of sapphire for the substrate of the GaN devices.
When solid GaN material is heated, the GaN is directly sublimed instead of giving a GaN melt. It is impossible to make a GaN melt which would allow the ordinary Czochralski method. It is said that ultrahigh pressure would be able to make an equilibrium state between the liquid phase and the solid phase of GaN. It is difficult to produce a GaN single crystal of a practical size in the ultrahigh pressure growing apparatus. Even if a single crystal of GaN were made, the crystal would be very small. Such a small GaN crystal is inappropriate for the substrates of making LEDs or LDs. A large sized ultrahigh pressure growing apparatus is necessary to making a large sized GaN single crystal in the equilibrium state, which prevents producing GaN single crystals on an industrial scale.
The Inventors have contrived a new method of growing a GaN crystal via a mask having windows on a GaAs (gallium arsenide) substrate in vapor phase for reducing the dislocations. This method is called a xe2x80x9clateral overgrowth methodxe2x80x9d or a xe2x80x9clateral growth methodxe2x80x9d.
{circle around (1)} Japanese Patent Application No.9-298300 (298300/""97) and
{circle around (2)} Japanese Patent Application No.10-9008 (9008/""98) proposed the lateral overgrowth method by the Inventors. The lateral overgrowth method makes a GaN crystal by forming a mask with dot windows or stripe windows on a GaAs substrate and growing a GaN crystal through the windows on the GaAs substrate. The method aims at producing a single crystal GaN wafer.
{circle around (3)} Japanese Patent Application No.10-102546 (102546/""98) proposed an improved method of making a plurality of GaN wafers by employing the GaN single crystal wafer produced by {circle around (1)} or {circle around (2)} as a seed, growing a thick GaN crystal ingot upon the GaN seed and slicing the ingot into a plurality of thin GaN wafers. The new method enables the Inventors to produce GaN substrates on an industrial scale.
GaN has cleavage which will solve the difficulty of dicing a processed wafer into individual chips. An n-type GaN substrate enables device makers to make LED film structures on the n-GaN substrate and forming n-electrodes on the bottom surface of the GaN substrate. The electrode design requires a smaller chip area than the sapphire substrate which allocates two electrodes upon the chip horizontally. The vertical electrode allotment saves one bonding wire per chip. The GaN substrates are profitable for making LEDs. In the case of making LDs, the resonator will be made by the natural cleavage. The GaN crystals cannot be a substrate for producing laser diodes (LDs) yet for some reasons.
The search for making blue light or violet light laser diodes has been clarifying the fact that the largest problem is to reduce the defect density in the GaN substrate. The defects, e.g., dislocations turn out to have a strong influence upon the lifetime or the properties of LDs because the LD is used under a severe condition of high current density. Prolongation of the lifetime of LDs, in particular, requires reducing the defect density in the GaN substrate.
Even the newly contrived lateral overgrowth method cannot decrease the defect density to a low level of less than 1xc3x97107 cmxe2x88x922 yet. Blue light LDs can be made upon the GaN substrate of the defect density of about 1xc3x97107 cmxe2x88x922. The lifetime is so short that the LDs cannot be used for practical use. Long lifetime GaN LDs require reducing further the defect density to a low level of less than 1xc3x97106 cmxe2x88x922. Namely, the dislocation (EPD; etch pit density) should be further reduced to the low level of less than 1xc3x97102 cmxe2x88x922. Here, the long lifetime of the LDs means a time longer than 10000 hours.
A first purpose of the present invention is to provide a low dislocation density GaN crystal of less than 1xc3x97106 cmxe2x88x922. A second purpose of the present invention is to provide a method for growing a low dislocation density GaN crystal of less than 1xc3x97106 cmxe2x88x922.
The Inventors have investigated the methods proposed for growing a GaN crystal in vapor phase for giving an effective solution to the above mentioned problems. The lateral overgrowth method which is the object for the investigation is explained by
{circle around (4)} EIC, vol.J81-C-II, No.1, p58-64(January 1998), and
{circle around (5)} Akira Sakai, Akira Usui, xe2x80x9cReduction of dislocation density in GaN films by epitaxial lateral over growthxe2x80x9d, J.J.Appl. Phys., vol.68, No.7, p774-779(1999). FIG. 14 to FIG. 17 show the steps of the lateral overgrowth.
FIG. 14 shows the section of a sapphire substrates, a GaN thin film piled on the substrate (which can be omitted), and a mask 2 with stripes 3 extending in the [11{overscore (2)}0] direction on the thin GaN film. The masked sapphire substrate is introduced into a furnace for growing a GaN layer on the substrate 1. As shown in FIG. 15, the GaN growth is selectively initiated on the exposed parts of the sapphire within the windows 3. The GaN film does not pile on the mask 2. (11{overscore (2)}2) planes, ({overscore (1)}e{overscore (1)}22) planes dominantly grow within the windows 3. Triangle-sectioned ridges 4 are formed along the stripe windows 3 having the (11{overscore (2)}2) planes and the ({overscore (1)}{overscore (1)}22) planes. The GaN film takes over the dislocations from the substrate. Vertical lines 6 show the dislocations which grow upward in parallel with the direction of growth in the GaN film.
When the windows are filled with the triangle ridges 4, the GaN layers protrude from the windows and extend horizontally over the mask 2 as shown in FIG. 16. During the horizontal growth, the heights of the layers are kept at a constant. The frontiers are facet planes 9 of (11{overscore (2)}2) and ({overscore (1)}{overscore (1)}22). The frontier facets 9 extend horizontally. The direction of the extension of dislocations turns to the horizontal directions. Horizontal lines 7 show the horizontal dislocations.
In the meantime, the GaN grains growing horizontally from neighboring windows meet at the middle points and unite soon together. The facets of (11{overscore (2)}2) and ({overscore (1)}{overscore (1)}22) vanish. The surface of the united GaN grains becomes smooth and flat. The dislocations are gathered into the middle planes 11 as shown in FIG. 17. The planes 11 are called xe2x80x9cdefect assembly planexe2x80x9d. Then, the GaN crystal grows in two-dimension on c-plane (0001), keeping a mirror flat surface 10. It is not easy to maintain the mirror-plane growth. But they believe that the mirror-plane growth should be kept even at the intermediate steps for making a flat smooth GaN single crystal. Fine regulation of the gas pressures, gas supplies and temperature keeps the flat smooth surface of the GaN crystal. FIG. 17 shows the smooth flat surface of c-plane (0001) after the integration of the grains.
Someone reports the fact that the penetration dislocations are reduced in the overgrowing grains extending horizontally over the mask on which the extending directions of the dislocations are horizontal as shown in FIG. 16. {circle around (5)} gave attention to the reduction and considered the ground of the reduction of dislocations over the mask. The following is the explanation given by {circle around (5)}. When the crystal grows in the c-axis direction with a c-plane surface, the dislocations extend in the c-axis direction. The penetration dislocations continue in the c-axis direction. The extension of the penetration dislocations follows the direction of the growth in many cases. When the GaN crystal grains grow in the horizontal direction over the mask, as shown in FIG. 16, the penetration dislocations turn to the horizontal directions. The turn of the extending directions would reduce the density of the penetration dislocations along the c-axis.
The previous report {circle around (5)} tells us that the GaN crystals grow in the vertical direction within the windows on the GaAs substrate, the crystals start to grow in the horizontal directions over the mask and the grains expanding from the neighboring windows are integrated together at the middle lines. Planar defect assemblies 11 are formed on the integration lines as shown in FIG. 17. The planar defect assemblies diminish as the thickness of the flat crystal increases. {circle around (4)} says, when the thickness increased over 140 xcexcm, the planar defect assemblies are extinguished. Then, {circle around (4)} insists that they succeeded in reducing the EPD of GaN below 107 cmxe2x88x922 by the lateral overgrowth method based upon the mask with windows.
The Inventors of the present invention made GaN crystals by the lateral overgrowth method and scrutinized the details of the growth. In the following description, the word xe2x80x9cfacetxe2x80x9d means any faces except the c-plane (0001) surface for discriminating slanting growths from the vertical growth on the c-plane (0001).
The grains extending from the windows are integrated with at a thickness of about 6 xcexcm. Then, the crystal grows in two dimensions vertically on the flat c-plane, piling c-planes one by one. The two dimensional growth maintains the mirror flatness of the surface. The Inventors made various GaN crystals from a 0.2 mm thickness to a 0.6 mm thickness. The lateral overgrowth method decreased the dislocation density till about 1xc3x97107 cmxe2x88x922. However, the method could not reduce the dislocation to low density of less than 1xc3x97107 cmxe2x88x922. The GaN crystals were not good enough to be a substrate for making LDs.
The Inventors have considered the reason why the dislocations do not decrease below 1xc3x97107 cmxe2x88x922 as follows. As long as the GaN crystal continues the simple two-dimensional growth in the c-axis direction keeping the flat mirror surface, the penetration dislocations bluntly extend in the c-axis direction, following the growth. The dislocations freely expand upward with the progress of the c-axis growth. There is no function of eliminating the dislocations in the two-dimensional c-axis growth. The c-axis growth keeping a flat smooth c-plane cannot annihilate the dislocations which have once been borne.
Another problem accompanies the prior mirror surface growth which grows the GaN crystal at a constant speed in the c-axis direction. The mirror surface growth has a drawback of requiring high temperature. The high temperature gives serious damage to the GaAs substrate which is weak to heat. The high temperature incurs no problem for the conventional sapphire substrate which has far higher resistance against heat than GaAs. However, the GaAs substrate requires lower temperature than the conventional sapphire substrate. The Inventors prefer the GaAs substrate to the sapphire substrate for the mentioned reasons. Besides, the GaAs substrate can be easily removed by etching after the GaN growth unlike the sapphire which cannot be eliminated due to the chemical stubbornness.
The consideration should be returned to the problem of the dislocations. The reduction of the dislocations requires some special device for annihilating the dislocations which have once been generated. The prior c-axis growth keeping the mirror c-plane has no device of annihilating the dislocations.
The Inventors hit on an idea of installing a dislocation-annihilation device in growing crystals and maintaining the dislocation-annihilation device during the growth for reducing the dislocations. The dislocation-annihilation device is a new concept which characterizes the present invention. The dislocation annihilation device reduces the dislocation density by killing the dislocations during the crystal growth.
The Inventors have investigated and found the method which enables us to originate the dislocation-annihilation device, grow a GaN single crystal under the influence of the dislocation-annihilation device and reduce the dislocations.
The present invention denies the prior two-dimensional growth of keeping the mirror flat c-plane surface but proposes a facet-keeping growth of making facets, keeping the facets and annihilating dislocations by the facets. The facets were previously defined as any planes on the surface except the c-plane. The facets are slanting planes on the growing surface except the c-plane. The dislocation-annihilation device is the facets. The Inventors have discovered a novel fact that the facets have the function of annihilating the dislocations. Nobody has suggested the function of the facets before the Inventors. The prior two-dimensional mirror surface growth denied the facets since the facets are origin of rugged surface and are the enemy of the mirror surface growth. On the contrary, the present invention positively produces the facets by controlling the condition of the growth and annihilates dislocations by the function of the facets. The facets correspond to some low index planes. Since GaN crystal has hexagonal symmetry, the facets belonging to the same collective index planes represent different slanting directions with the same slanting angle to the c-axis. Neighboring facets have a boundary. The facet-keeping growth gathers the dislocations to the boundary. The facet boundary forms a xe2x80x9cdislocation accumulating planexe2x80x9d. The crossing point of the dislocation accumulating planes makes a xe2x80x9cdislocation bundle linexe2x80x9d which accumulates plenty of dislocations. The facets kill the dislocations. The dislocation-annihilating device is the facets in the present invention. The exploitation of the facets enables the present invention to reduce the dislocation density to less than 106cmxe2x88x922 which is about one tenth of the prior method. Surprisingly, the present invention allows us to make a low-dislocation GaN single crystal of about 104 cmxe2x88x922 to 5xc3x97103 cmxe2x88x922.
The facet is not a c-plane but a plane which is not orthogonal to the growing direction (c-axis). The prior method makes efforts to grow a GaN crystal, keeping a flat, smooth surface of the c-plane without facets. The facets are undesirable defects for the prior method. The prior method excludes the facets. The present invention recommends the generation of the facets, distributes the facets uniformly and reduces the dislocations by the facets to the contrary. The present invention succeeds in producing low-dislocation GaN crystals by exploiting the function of the facets. Low-dislocation GaN substrates can be produced by cutting the low-dislocation GaN crystal made by the present invention into thin wafers. The substrates are the best GaN substrates for blue light lasers (LDs) or violet light lasers (LDs).
The method of the present invention includes the conditions of:
(1) generating facets and growing a crystal without vanishing the facets till the end of the growth,
(2) keeping boundaries between the neighboring facets and
(3) maintaining dislocation-accumulating planes as sets of cross points of the facets.
These restrictions enable this invention to succeed in producing a low-dislocation GaN single crystal of dislocation density of less than 106 cmxe2x88x922 for the first time.
The fundamental idea is rather difficult to understand. Thus, the present invention requires detailed explanation. Facets are low-index planes except the c-plane which is the growth surface, since the growth is done in the c-axis direction. All the planes of the grains on the surface except the c-plane are facets. The definitions of the planes, the directions and the indexes are now clarified.
GaN (gallium nitride) crystal belongs to the hexagonal symmetry group which has six-fold rotation symmetry around the c-axis. Four index number is now employed to describe planes and directions on crystallography. The a-axis and b-axis are vertical to the c-axis. The a-axis inclines at 120 degrees to the b-axis. The length of the a-axis is equal to the length of the b-axis (a=b). The length of the c-axis is not equal to the length of the a-axis or b-axis (axe2x89xa0c). Besides the a-axis and b-axis, an extra d-axis is assumed on the ab-plane for giving rotational symmetry to the mirror indexes. The d-axis inclines at 120 degrees to the a-axis and at 120 degrees to the b-axis. A rotation of 120 degrees on the c-axis moves the a-, b-, d-axes to the b-, d-, a-axes respectively. Since the extra d-axis has been introduced for giving rotation symmetry to the indexes, the three indexes are not independent. One set of parallel planes are denoted by a mirror index (klmn). The index (klmn) means that the first plane cuts the a-axis at a/k, the b-axis at b/l, the d-axis at d/m and the c-axis at c/n. The definition of the mirror index is common to other symmetry groups. Since the a-, b- and d-axes are included in the ab-plane, the numbers k, l and m are not independent. Three indexes k, l and m always satisfy a sum rule of k+l+m=0. The three index numbers have rotational symmetry. The rotational symmetry is equivalent to the sum rule of k+l+m=0.
Individual planes should be denoted by a round bracket ( . . . ). Collective planes should be denoted by a wavy bracket { . . . }. The xe2x80x9ccollectivexe2x80x9d means a set of all individual planes which can be interchanged with another member by the symmetry operations allowed by the crystal group. The direction is denoted by the same mirror index as the plane perpendicular to the direction. Individual directions should be designated by a square bracket [ . . . ]. Collective directions should be denoted by a triangle bracket  less than  . . .  greater than .
GaN crystal is grown in the c-axis direction on the c-plane which has six equivalent axes. The facets are defined as planes except the c-plane (0001). If any of k, l and m of a plane is not zero, the plane is a facet on the surface. There are, however, some distinctions among the facets. Some facets are apt to appear on the surface. But other facets do not easily appear on the surface. Important facets which often appear on the growing crystal are {1{overscore (2)}12}, {1{overscore (2)}11}, {n{overscore (2)}nnk} (n,k=integer), {1{overscore (1)}01}, {1{overscore (1)}02}, {n{overscore (n)}0k} (n,k=integer),
Here, {1{overscore (2)}12} means that k=1, l=xe2x88x922, m=1, n=2. As explained before { . . . } signifies collective planes. For example, {1{overscore (2)}12} includes six equivalent planes (1{overscore (2)}12), (2{overscore (1)}{overscore (1)}2), (11{overscore (2)}2), ({overscore (1)}2{overscore (1)}2), ({overscore (2)}112) and ({overscore (1)}{overscore (1)}). The six planes form a six-fold concave on the surface. However, the six individual indexes are not written hereinafter for simplicity. The six planes building the six-fold concave are simply denoted by {1{overscore (2)}12}. The facets {1{overscore (2)}12} signify the six equivalent facets. On the contrary, other expressions {2{overscore (1)}{overscore (1)}2)} or {11{overscore (2)}2)} are equivalent to {1{overscore (2)}12}.
The fundamental principle basing the present invention is reduced to the function of the facets of sweeping and gathering defects, e.g., dislocations, to the boundaries (dislocation accumulating planes) of different index facets or gathering the defects to the center line (dislocation bundle line) of the different index facets.
Since the dislocations are swept and gathered to the boundaries of the facets and the center lines of the facets, the dislocations existing in other parts are reduced to the contrary. The quality of the crystal is enhanced by the reduction of the dislocations. However, the number of the dislocations localized at the boundaries (dislocation accumulating planes) and the central lines (dislocation bundle line) is increasing. The above is a brief explanation of the principle of the present invention.
A more detailed explanation is given from now. It may be difficult to understand the ground that the facets have the function of gathering the dislocations. At first, the change of the dislocation expansion is explained. Then, the accumulation of the dislocations is clarified.
The direction of the extension of dislocations depends upon the direction of the crystal growth. In the case of GaN crystal, the dislocations progress in the c-axis direction when the GaN crystal is growing two-dimensionally in the c-axis direction within the mask windows. However, when the top of the crystal rises over the mask thickness, the grain frontier begins to extend in the horizontal directions on the mask. When the growing direction is changed to the horizontal mode, the extending directions of the dislocations are also changed into the horizontal directions. The prior art of the lateral overgrowth method reported the horizontal extension of the dislocations in the horizontal growth on the mask. Namely, the direction of the extension of the dislocations follows the direction of the crystal growth.
The steps of the lateral overgrowth are again considered by referring to FIG. 14 to FIG. 17. FIG. 14 shows a starting substrate 1 having a mask 2 with windows 3. FIG. 15 shows a intermediate state in which GaN grains 4 grow only on the exposed GaAs substrate 1 within the isolated windows 3. The GaN grains 4 cannot grow on the mask 2. The grains 4 are triangle-sectioned cones having slanting planes 5 (facets). Dislocations 6 extend upward in the cones as depicted by narrow lines. The slanting angles of the facets 5 are predetermined. When the GaN cones 4 fill the windows 3, the GaN crystal grow over the windows 3 and ride on the mask material 2 as shown in FIG. 16. Frontier facets 9 progress in the horizontal directions in the ab-plane on the mask 2, keeping a definite slanting angle. The vertical dislocations 6 turn to be horizontal dislocations 7 at turning planes 8 and extend in the horizontal directions. Soon neighboring GaN grains come into contact at the middle planes between the windows. The facet frontiers 9 collide with together and vanish at the middle planes. The dislocations 7 end on the meeting planes 11. The middle planes 11 include plenty of dislocations. Some dislocations vanish on the middle planes 11. Then, the direction of the GaN crystal growth turns again. GaN crystal 10 begins to grow in the vertical direction, keeping a flat, mirror-smooth surface of a c-plane.
In stead of the mirror surface growth without facets of FIG. 17, this invention prefers a rugged surface growth having plenty of facets in the c-axis direction. This invention denies the prior mirror-surface growth but chooses a rugged, rough surface growth accompanied with many facets and with boundaries. The boundary is defined as the crossing line at which two facets meet together. Since the facet is a plane, the boundary is a straight line. A six-folding facet cone has six boundaries. There are two cases for the crossing angles between the neighboring facets.
(1) In the case of a facet-crossing angle below 180 degrees (FIG. 1)
The first case is that the crossing angle between the neighboring facets of different indexes is less than 180 degrees. FIG. 1 shows an example of the crossing angle of less 180 degrees. A pyramid having four slanting planes Fa, Fb and so on is put on a square column. The number of facets is arbitrary. Typical facet number of the pyramid is six or twelve from the symmetry. But other sets of facet numbers sometimes exist. The set of the facets is called a convex-type which projects as a pyramid on the growing surface. The crossing angle is defined as the inner crossing angle between the facets. The convex-type set has a crossing angle below 180 degrees. Two facets Fa and Fb shown by hatched lines have a crossing line m. The average growth direction is the c-axis direction.
Individual growing directions on the facets Fa and Fb are denoted by arrows A and B. Namely, the individual growing directions A and B are obtained by projecting the normals standing on the facets Fa and Fb from the bottom planes. The dislocations expand in the same directions as the individual growing directions A and B. The dislocations direct outward on the convex pyramid. The dislocations separate farther from the boundary m. Since the dislocations disperse outward, the dislocations do not cross each other, as shown in FIG. 2. The crystal growth succeeds the undercoating crystal. The difference of the indexes may induce difference of the impurity concentration on the different planes. The crystal takes over the defects of the undercoating crystal. The number of the dislocations is not changed. FIG. 3 shows a state of the convex type facets set. The height uniformly increases without changing the shape. The dislocations do not reduce. Namely, the crossing angle below 180 degrees has no function of reducing the dislocations.
2 In the case of a facet-crossing angle over 180 degrees (FIG. 4)
The second case is that the crossing angle between the neighboring facets of different indexes is more than 180 degrees. FIG. 4 shows an example of the crossing angle of more than 180 degrees. A part of a concave having several slanting planes Fa, Fb and so on is depicted. The number of facets of a concave is arbitrary. Typical facet number of the concave is six or twelve from the symmetry. But other sets of facet numbers sometimes exist. The set of the facets is called a xe2x80x9cconcave-typexe2x80x9d which makes many holes on the growing surface. The concave-type set has a crossing angle over 180 degrees. Two facets Fa and Fb shown by hatched lines have a crossing line m. The average growth direction is the c-axis direction. Individual growing directions on the facets Fa and Fb are denoted by arrows A and B. Namely, the individual growing directions A and B are obtained by projecting the normals standing on the facets Fa and Fb from the bottom planes. The dislocations move in the same directions as the individual growing directions A and B. The dislocations direct inward in the concave. The dislocations are swept into the boundary m by the progress of the individual growth. The dislocations finally reach the boundary m. The boundary m is shot by the dislocations moving from two facets. The dislocations are stopped at the boundary m. The dislocations cannot extend further on the other facet. Since the facets are concave, the dislocations are swept and gathered at the boundary m as shown in FIG. 6. Then, the dislocations turn down along the boundary m. The boundary accumulates the dislocations.
Since the crystal growth continues in the c-axis direction, the boundary forms a plane at the middle of the facets as shown in FIG. 6. The dislocations are accumulated and buried in the middle plane K which is called a defect accumulating plane K The defect accumulating plane K grows upward according to the progress of the growth. The defect accumulating plane K can be a small angle grain boundary. The defect accumulating plane K is a bisecting plane between the neighboring facets Fa and Fb.
The dislocations on the facets are gradually absorbed by the defect accumulating planes K and are vanishing from the facets. The dislocations further progress slantingly downward from the defect accumulating planes K to the central axial lines. As the crystal growth continues, the defects are swept and gathered into the central axial lines of the set of the facets. This is the principle on which the present invention is based. A set of the facets of above 180 degree crossing angle have such a defect annihilating effect, as explained by FIG. 4 to FIG. 6.
Then, the case of the facets having a common accumulating line is explained. FIG. 7 shows a more concrete set of facets forming a pit than FIG. 4, FIG. 5 and FIG. 6. Practical experiment of growing GaN crystal shows us that the convex-type facets of FIG. 1 to FIG. 3 do not appear at all but the concave-type facets of FIG. 4 to FIG. 6 do appear on the GaN growing crystal surface. The convex-type facets of FIG. 1 to FIG. 3 which would disperses dislocations does not occur in practice. This is a happy asymmetric phenomenon. This invention makes the best use of the fortunate asymmetry.
FIG. 7 shows a six-fold reverse-cone pit EGHIJN-D having facets of {1{overscore (2)}12}. The average growth S is directed upward in the c-axis direction. In the six-fold pit, individual growing directions A, B . . . are normal to the facets as shown by arrows or the inward directions from the facets to the central axial line. Dislocations accompany the growing direction. Since the individual growth is direct inward, the dislocations expand also inward as shown in FIG. 8. The six facets grow at a common speed. The dislocations attain at the boundaries between m the facets.
Another problem is whether these dislocations would cross the lines K and extend into the neighboring facets. The facet Fb has the individual growing direction B and the dislocation-extending direction b which is parallel with B. If the dislocations moving from the facet Fa would be assigned to the dislocations of the facet Fb, the dislocation S should turn the moving direction at an angle of 60 degrees. The 60 degree turn is impossible for the dislocations. The dislocations follow the growth. The dislocations cannot jump to the neighboring facets. The dislocations either vanish on the boundary or survive in the boundary m. Since the boundaries are abnormal lines in the growth, the boundaries admit the dislocations to invade in the lines. But the dislocations cannot escape from the boundaries again.
In practice, the average growth is direct upward. The hexagonal pit is buried by the newly-growing crystal. However, the pit does not diminish, because the top aperture has a tendency of widening. The tendency of widening balances with the upward growth. Thus, the hexagonal pit moves upward without diminishing. V denotes the growing speed in the c-axis direction. The slanting angle of the facet is designated by xcex8. If the growing speed of the facet in the normal direction is V sin xcex8, the pit is slightly upward displaced at the speed of V without deforming. As sheets of crystal is piled, the previous dislocations are buried in the boundaries. The boundaries gather and hold many dislocations. Since the dislocations are swept, gathered and maintained in the boundaries, the dislocation density decreases at other parts.
The dislocations are stored in the bisecting planes between the neighboring facets. The planes are called xe2x80x9cdefect accumulating planesxe2x80x9d K. FIG. 9 shows the planes K. The defect accumulating planes K are rotationally symmetric on the central axis of the pit, meeting each other at 60 degrees.
Since the average growth progresses upward, the dislocations on the boundaries move toward the central line. Namely, the dislocations seem to slide down along the boundaries to the central line. The line which is a locus of the xe2x80x9cmultidefect pointsxe2x80x9d D including plenty of dislocations is called a xe2x80x9cdefect accumulating linexe2x80x9d L.
Many dislocations moving from all the facets in the pit and small-angle grains are unified and integrated at the multidefect point D. Then nearly all of the defects on the facets in the pit are gathered to the multidefect point D. Some defects vanish in the meantime of the movement. All the other defects are collected to the multidefect point D.
As the vertical growth continues, the defects are left in the vertical line (defect accumulating line L) extending below the current multidefect point D. The six boundaries leave similarly six defect accumulating planes K and the small-angle grains as the growth progresses.
The planar defects groups (defect accumulating planes) K, the small angle grains and the linear defect assemblies (defect accumulating lines) L remain in the growing crystal. Defects are condensed into the linear or planar defect assemblies. However, the total of the defects surely decreases. Some of the dislocations vanish when they meet the boundaries. Some dislocations are extinguished when the boundaries meet the central linear defect lines L. Some defects are annihilated by interactions when they are compressed in a narrow space in the defect assembling lines L or the defect assembling planes K. For example, a collision of blade-type dislocations kills the dislocations. The defects decrease with the progress of the growth.
The formation of the defect accumulating planes K and defect accumulating lines L depend upon the condition of the growth. Optimization of the growing conditions enables the crystal to decrease the planar defect assemblies K and linear defect assemblies L. Selection of the growing condition can vanish the small angle grains and planar defect assemblies. In this case the crystal has a good property.
On the contrary, other choice of the growing conditions positively produces the planar defects assemblies, linear defect assemblies and small angle grains which gather many individual defects. The linear defect assembly is counted as one defect in the EPD (Etch Pit Density) measurement. The generation of the linear defect assemblies has an effect of reducing the measured defect density. For example, if one multidefect point includes about 10000 dislocations, the EPD seems to decrease to one thousandth ({fraction (1/1000)}).
The method of decreasing defects of the present invention has been clarified hitherto. An important problem is still left unexplained. The reduction method explained till now is restricted to the region at which facets exist because the reduction is originated from the facet growth. If the crystal surface includes smooth, flat c-axis growing parts without facets, the flat regions would be free from the function of reducing defects. The normal c-axis growth expands parallely dislocations in the c-axis direction without reducing the dislocations.
FIG. 11 shows a section of a growing GaN crystal. The upward arrow denotes the growing direction or time. The height z increases as a function of time. Thus, the height of the crystal is equivalent to time of the growth. The hatched parts (s) denote the c-axis growing regions. The blank parts (w) show the facet-growing regions. FIG. 11 denotes the sections of the smooth, flat c-axis growing regions (s) and the rugged facet-growing regions (w). FIG. 11 shows the case assuming the unchanging sections of the flat c-axis growing regions and the rugged facet-growing regions. This is only an imaginary scheme for facilitating the explanation. The boundaries (q) are between the smooth c-axis growing regions (s) and the rugged facet-carrying growth regions (w). In the case, the boundaries (q) are parallel with the direction of the growth. The regions (w) with the facets have the dislocations reduction effects. The regions (s) have no effect of reducing the dislocations. The initial EPD in the crystal is denoted by xe2x80x9cQxe2x80x9d. The EPD is kept in the hatched regions (s) ruled by the smooth c-axis growth. Even if the EPD is reduced to zero at the white regions (w) of the facet-growth, the final EPD would be restricted to EPD=Qs/(s+w), where s is the sectional area of the hatched region of the c-axis growth and w is the sectional area of the blank regions of the facet-growth. The reduction ratio of the EPD would be only s/(s+w). The ratio is about 1/2 or 1/3 at most. But it is not the fact. The reduction rate of the present invention is about {fraction (1/10000)}.
This invention can offer a sophisticated solution for reducing drastically the EPD.
The formation of the facets depends upon the conditions of growth. For example, the partial pressure of NH3, the growing speed of GaN, the growing temperature and the gas supply mode rule the formation of facets. This invention generates facet-growth and maintains the facet-growth by controlling the growth conditions in the manner for forbidding the mirror-surface growth. The present invention prefers the facet-growth to the mirror surface growth. This invention entirely contradicts to the prior GaN growing method which prefers the smooth mirror-surface growth.
The mirror-surface growth (conventional) and the facet-driven growth (this invention) can be selected by the growing conditions. For example, higher temperature is liable to induce the mirror-surface growth and has a tendency of preventing the facet-driven growth. Lower temperature is apt to realize the facet growth in stead of the mirror growth. Slower speed of growth has a tendency of causing the mirror-surface growth. Faster growing speed is liable to induce the facet growth. Lower NH3 partial pressure is favorable for the mirror-surface growth. The facet-growth can be triggered by enhancing the NH3 partial pressure. Lower HCl partial pressure prefers the mirror-surface growth. Enhancement of the HCl partial pressure facilitates the facet-growth. In general, the favorable conditions for the facet growth are contrary to those for the mirror-surface growth. The determination of the conditions reverse to the mirror-surface growth can realize the facet-growth in general.
The present invention tries to allocate at least one experience of the facet-driven growth to all the longitudinal regions (columns) divided along the growing (thickness) direction by changing the growing conditions in various ways. The fact that the divided longitudinal regions (columns) have an experience of the facet-growth is now called the xe2x80x9cfacet growth hysteresisxe2x80x9d. Any column having once the facet growth hysteresis can exclude the seeds of dislocations by the facet-growing. The column is cleaned by the facet-growth. Once cleaned column is immune from the dislocations, even if the column part begins the mirror-surface growth, because the column has no seeds of dislocations. Allocation of the facet-growth hysteresis to all the columns imagined in the crystal can make a low-dislocation crystal as a whole. This invention reduces the dislocations of all the regions by allotting all the regions the facet-growth hysteresis. This is an excellent feature of the present invention. The gist of the present invention is again clarified more rigorously. The three dimensional coordinate is defined. The vertical coordinate is denoted by xe2x80x9czxe2x80x9d. Since the crystal grows in the upward direction, the time of growth is equivalent to the z-coordinate of the surface. The surface of the substrate is denoted by the x- and y-coordinates. Thus, three dimensional coordinate (x,y,z) is defined in the GaN growing crystal. A three-dimensional facet-characteristic function w(x,y,z) is introduced for clarifying the explanation. If the point (x,y,z) is the facet-growing part, w(x,y,z) is 1. If the point (x,y,z) is the mirror-growing part, w(x,y,z) takes 0. Namely,
w(x,y,z)=0 for point (x,y,z) of mirror-surface growth
w(x,y,z)=1 for point (x,y,z) of facet-driving growth.
For example, in FIG. 12, the hatched regions (s) give w(x,y,z)=0 and the blank regions (w) give w(x,y,z)=1. Thus, w(x,y,z) is a localized function at a point (x,y,z). Now a two-dimensional hysteresis function W(x,y) is further defined upon the facet-characteristic function w(x,y,z). A normal line is projected from an arbitrary point (x,y) on the surface to the bottom of the crystal. If the normal line passes points of w(x,y,z)=1 at least one time, the hysteresis function W(x,y) is defined to be 1. If the normal line does not meet a point of w(x,y,z)=1, the hysteresis function W(x,y) is defined to be 0. In other words, if there is at least a point (x,y,z) of w(x,y,z)=1 for 0xe2x89xa6zxe2x89xa6H (height of the crystal), the hysteresis function W(x,y) for the (x,y) is determined to be 1. If there is no point (x,y,z) of w(x,y,z)=1 for 0xe2x89xa6zxe2x89xa6H (height of the crystal), the hysteresis function W(x,y) for the (x,y) is defined to be 0.
W(x,y)=maxz{w(x,y,z)}
where maxz means taking the maximum value for a variable z from z=0 to z=H. If the hysteresis function W(x,y) is 1, the column (x,y) has a facet-growth part at some point from z=0 to z=H of the two-dimensional point (x,y). If all the surface points (x,y) has W(x,y)=1, all the points have the facet-growth hysteresis at some height z.
FIG. 12 shows the section of an example having fluctuating facet-growing regions and mirror-surface growing regions. The blank parts are facet-growing regions which have the function of annihilating dislocations. The hatched parts are mirror-surface growing regions which have no function of reducing dislocations. The example of FIG. 12 has wide facet-growing regions at the beginning. The facet-growing regions have already absorbed dislocations as planar defect assemblies and linear defect assemblies. If the mirror-surface c-axis growth succeeds, the facet-growth, dislocations do not extend any more, since the dislocations have been annihilated. In FIG. 12, any regions preceded by the blank regions are immune from dislocations. Thus, even if the hatched regions of the mirror-surface growth dilates at a later step, the low-dislocation is maintained in the GaN crystal. The reduction of the dislocations is not directly proportional to the rate of the facet-growing regions at some height but proportional to the rate of the facet-growing hysteresis regions.
FIG. 13 shows another example of more an extreme case having a height in which all the parts are facet-growing regions (w) at an early stage. At the horizontal level, facet-growing occurs at all the parts and dislocations are decreased by the facet-growth. Once the dislocations are annihilated at the level. Even if the mirror-surface growth follows some parts, the mirror-surface growth does not transcribe the dislocations since the seeds of the dislocations have been excluded there. Horizontal fluctuations of the facet-growing regions positively reduce the dislocation density all over the surface by annihilating the sees of the dislocations at some height of the imaginary columns. It is desirable that the facet-growing regions move in the horizontal directions for decreasing the defects.
A columnar region would have little dislocation density so long as the region has the facet-growing hysteresis at some height. The etch pit density at a time (t) or at a height (z) is not determined by the distribution of the facet-growing regions and the mirror-surface growing regions at the present height. If a region having a facet-growth experience is growing in the mirror surface at present, the regions can be low dislocation density. The dislocations density is ruled by the distribution of the facet-growing hysteresis. The facet-maintaining growth sweeps and decreases the dislocations to the multidefect planes (defect accumulating planes) K or the defect-accumulating lines L. If the defect-annihilating function were restricted at the present surface of the growing crystal, the dislocation density would simply be decreased to a rate of (Wxe2x88x92F)/W, where W is the total area, F is the facet-growing area and (Wxe2x88x92F) is the mirror-growing area. Since (Wxe2x88x92F)/W is a number of an order of 1, the drastic reduction of an order of 10xe2x88x924 to 10xe2x88x923 would not occur. The magical reduction is encouraged by the vertical history of the facet-growth in any imaginary columns. If a vertical column has an experience of the facet-growth at a time, the column enjoys the merit of the low dislocation density in future. The surprising reduction of an order of 10xe2x88x924 to 10xe2x88x923 results from the fact that the memory of the facet-growth for decreasing the dislocations is maintained in the vertical directions.
It is preferable to give the facet-growing hysteresis at an early stage of growth. In the case of making a long crystal ingot, an early facet-growing experience is effective for producing a good crystal having low density of dislocations. In any virtual vertical columns, the initial mirror-growing portions have high density of dislocations, a facet-growing occurs some time, and low dislocation density portions follow the facet-growing regions.
The facet-maintaining growth is realized by the operation of decreasing the temperature, enhancing the HCl partial pressure, raising the NH3 partial pressure, or heightening the growth speed. The facet-growth hysteresis is given to all the vertical virtual columns by one or a couple of the above-cited operations. Otherwise, an unintentional, natural change of growing conditions sometimes endows the portion with the facet-growth and the facet-growth hysteresis.
The present invention grows a GaN crystal, removing the dislocations. The GaN crystal made by the present invention includes planar defect regions, small angle grains and linear defect assemblies which contain plenty of dislocations. Other regions except the defect assembling portions contain little dislocations. The other regions are nearly dislocation-free. The GaN crystal ingots have low density of dislocations. The crystal property is improved. The wafers sliced from the GaN ingot are low-dislocation density wafers. The GaN wafers can be the substrates for making laser diodes (LDs).
The present invention explained hereto contains the fundamental ideas of;
(1) the reduction of dislocations by sweeping the dislocations to the boundaries between neighboring facets,
(2) the formation of the defect-accumulating planes by assembling the dislocations just below the boundaries,
(3) the prevention of the dislocations from diffusing by integration and accumulation of the dislocations at the confluences of the facets,
(4) the formation of the defect-accumulating lines below the confluences (multi-defect point) by the accumulation of the dislocations,
(5) the increment of the low-dislocation portions by the increase of the face-growth hysteresis regions.
These functions enable this invention to obtain low-dislocation GaN single crystal which is immune from dislocations except the defect-accumulating lines. The defect-accumulating lines is a bundle of dislocations. When the EPD (etch pit density) is measured by a microscope observation, one defect-accumulating line is counted as one etch pit. If a defect-accumulating line (linear defect assembly) is a bundle of about 104 dislocations, the formation of the defect-accumulating lines enables the present invention to decrease, for example, about 108 cmxe2x88x922 dislocations to about 104 cmxe2x88x922 dislocations. The reduction rate is about 10xe2x88x924.
The fundamentals of the present invention have been explained. Furthermore, details of the present invention will be clarified with reference to the restrictions of the claims. The present invention is a method of growing a low dislocation density GaN single crystal by the facet-driving growth generating and maintaining the facets throughout the process instead of the mirror-surface maintaining method. Namely, the GaN crystal is grown on the conditions making and keeping three dimensional facet structure and avoiding the mirror-surface growth.
The three-dimensional facet structure is a set of polygonal cones with facets or complexities of pits having facets.
The present invention suggests a method of growing a gallium nitride (GaN) single crystal maintaining the facet structure and reducing defects by producing defect accumulating planes which are vertical to the average growing surface.
The present invention proposes a method of growing a GaN single crystal maintaining the facet structure and reducing defects by producing defect-accumulating lines which are vertical to the average growing surface.
The facet structure contains polygonal pits. The pits have slanting side walls. The orientations of the side walls are mainly {11{overscore (2)}2}. Then most of the pits are hexagonal conical pits enclosed by the six equivalent {11{overscore (2)}2} planes. The neighboring { 11{overscore (2)}2} planes meet at nearly 120 degrees. With a lower probability, {1{overscore (1)}01} planes appear as pit walls. In the case, the pits are twelve-fold cones having six {11{overscore (2)}2} planes and six {1{overscore (1)}01} planes. The neighboring walls meet at nearly 150 degrees. Experiments teach us that sets of facets form concaves (pits) in most cases. The facet structure rarely produces convexes (protrusions). This is a favorable property for the present invention. As mentioned before, the convex facets have no function of reducing dislocations. Only the concave facets have the desirable function of reducing dislocations. The facets appearing frequently on the facet-driving growth are {11{overscore (2)}2}, {1211}, {n 2{overscore (n)} n k}(n, k; integers), {1{overscore (1)}01}, {1{overscore (1)}02}, {n {overscore (n)} 0 k}(n, k; integers).
The present invention further proposes a method of growing a low dislocation density GaN single crystal by producing and maintaining facets, making concaves (pits) of three dimensional facet structure, sweeping dislocations and assembling the dislocations in the defect-accumulating lines which are vertical to the average growing plane. When the facet structure is a hexagonal conical pit, the defect-accumulating line extends below from the bottom of the pit.
The present invention proposes moreover a method of growing a low dislocation density GaN single crystal by maintaining facets, making concaves (pits) of three dimensional facet structure, sweeping dislocations, assembling the dislocations in the defect-accumulating planes extending just below the boundaries of the facets and decreasing the dislocations.
The present invention further proposes a method of growing a low dislocation density GaN single crystal by maintaining facets, making hexagonal conical pits of three dimensional facet structure, sweeping dislocations on the facets, assembling the dislocations in the defect-accumulating planes extending radially from the axis and meeting together at 60 degrees.
The present invention further proposes a method of growing a low dislocation density GaN single crystal by maintaining facets, moving the facet-lying regions in the horizontal directions, giving facet-growth hysteresis to all the vertical columnar regions, and reducing the dislocations by making the regions experience the facet-growth.
Most frequently appearing facet planes are {11{overscore (2)}2} planes. In the case, the planar defect-accumulating assemblies have orientations of {11{overscore (2)}0}. Sometimes the defect-accumulating planes are small angle grains.
The important matter for the present invention is to maintain the facet structure during the growth. The direction of the growth is optional. For example, a low dislocation density GaN crystal can be grown in the {11{overscore (2)}0} directions or {1{overscore (1)}00} directions. The c-axis growth is the most effective for reducing the dislocations.
The dislocation reduction of the present invention requires more than 10% of the facet rate F/W of the three-dimensional facet-wearing area F to the total surface W of both the GaN crystal growing in the vapor phase and the GaN crystal grown up. Namely, F/Wxe2x89xa70.1. Here, the three dimensional facet structure includes the pits having facets and the assemblies of the pits.
A further reduction of the dislocations requires more than 40% of the facet rate F/W of the three-dimensional facet-wearing area F to the total surface W of both the GaN crystal growing in the vapor phase and the GaN crystal grown up. Namely, F/Wxe2x89xa70.4. The GaN crystal should be covered with the facet structure of the pits with wide areas for decreasing the dislocations by the facets.
A more effective reduction of the dislocations requires more than 80% of the facet rate F/W. F/Wxe2x89xa70.8. When the facet rate F/W is more than 80%, the growing pits come in contact with each other.
100% of the facet rate F/W accomplishes the maximum reduction of the dislocations. Namely, F/W=1. All the growing pits and the assemblies of the pits are in contact with each other. There is no c-plane part on the surface.
The above-mentioned relates to the crystal growth in which all the facets have clear orientations. The Inventors confirmed that even the case in which the facets having obscure orientations occupy the surface enjoys the dislocation reduction effect by the facets. For example, the Inventors examined the GaN growth case in which round hexagonal conical pits occupy the surface. The round pits have the power of sweeping and storing dislocations to the boundaries. Even the round pits have surely some boundaries between the facets and the boundaries gather dislocations.
This invention includes the case in which the growth pits and the assemblies of the pits on the surface after the vapor phase growth include curvatures deviating from the facets with definite crystal indices. The curvatures have the function of the eliminating dislocations from the curvatures to boundaries.
This invention further includes the case in which the growth pits and the assemblies of the pits on the surface after the vapor phase growth have more than 10% occupation rate on the surface and all the pits and the assemblies are built by the curvatures deviating from the facets with definite indices.
The desirable range of the diameters of the pits consisting of the facets or the complex pits as assemblies of the pits is 10 xcexcm to 2000 xcexcm. Too small diameter of the pits has poor effect of reducing the dislocations. Too big diameter of the pits is uneconomical by increasing the loss on the polishing process which eliminates the pits and obtains a smooth surface.
The minimum record of EPD of GaN crystals was 107 cmxe2x88x922. The present invention succeeds in making a low dislocation density GaN single crystal having EPD of less than 106 cmxe2x88x922. The present invention enables makers to produce low dislocation density GaN single crystals on an industrial scale. The low dislocation density GaN single crystal substrates allow device makers to make long lifetime, high quality, high power blue/violet light semiconductor laser diodes.